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  2. Angle - Wikipedia

    en.wikipedia.org/wiki/Angle

    In general, the measures of the interior angles of a simple convex polygon with n sides add up to (n − 2) π radians, or (n − 2)180 degrees, (n − 2)2 right angles, or (n − 2) ⁠ 1 / 2 ⁠ turn. The supplement of an interior angle is called an exterior angle; that is, an interior angle and an exterior angle form a linear pair of angles ...

  3. List of trigonometric identities - Wikipedia

    en.wikipedia.org/wiki/List_of_trigonometric...

    The angle difference identities for ⁡ and ⁡ can be derived from the angle sum versions by substituting for and using the facts that ⁡ = ⁡ and ⁡ = ⁡ (). They can also be derived by using a slightly modified version of the figure for the angle sum identities, both of which are shown here.

  4. Proofs of trigonometric identities - Wikipedia

    en.wikipedia.org/wiki/Proofs_of_trigonometric...

    The figure at the right shows a sector of a circle with radius 1. The sector is θ/(2 π) of the whole circle, so its area is θ/2. We assume here that θ < π /2. = = = ⁡ = ⁡ The area of triangle OAD is AB/2, or sin(θ)/2.

  5. Solution of triangles - Wikipedia

    en.wikipedia.org/wiki/Solution_of_triangles

    A general form triangle has six main characteristics (see picture): three linear (side lengths a, b, c) and three angular (α, β, γ). The classical plane trigonometry problem is to specify three of the six characteristics and determine the other three. A triangle can be uniquely determined in this sense when given any of the following: [1] [2]

  6. Small-angle approximation - Wikipedia

    en.wikipedia.org/wiki/Small-angle_approximation

    The red section on the right, d, is the difference between the lengths of the hypotenuse, H, and the adjacent side, A. As is shown, H and A are almost the same length, meaning cos θ is close to 1 and ⁠ θ 2 / 2 ⁠ helps trim the red away. ⁡

  7. Angle bisector theorem - Wikipedia

    en.wikipedia.org/wiki/Angle_bisector_theorem

    Consider a triangle ABC.Let the angle bisector of angle ∠ A intersect side BC at a point D between B and C.The angle bisector theorem states that the ratio of the length of the line segment BD to the length of segment CD is equal to the ratio of the length of side AB to the length of side AC:

  8. Angles between flats - Wikipedia

    en.wikipedia.org/wiki/Angles_between_flats

    If the flats do not intersect, their shortest distance is one more invariant. [1] These angles are called canonical [2] or principal. [3] The concept of angles can be generalized to pairs of flats in a finite-dimensional inner product space over the complex numbers.

  9. Corresponding sides and corresponding angles - Wikipedia

    en.wikipedia.org/wiki/Corresponding_sides_and...

    The corresponding angles as well as the corresponding sides are defined as appearing in the same sequence, so for example if in a polygon with the side sequence abcde and another with the corresponding side sequence vwxyz we have vertex angle a appearing between sides a and b then its corresponding vertex angle v must appear between sides v and w.